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Table 2 Accuracies in solution values in Example 5.2 with \(\pmb{\eta=100\pi,\delta=30 \pi^{2}}\)

From: A fourth-order accurate quasi-variable mesh compact finite-difference scheme for two-space dimensional convection-diffusion problems

L  + 1 \(\boldsymbol {\tilde{\alpha}}\) \(\boldsymbol {\tilde{\beta}}\) \(\boldsymbol {\mathcal{E}_{\infty}}\) \(\boldsymbol {\mathcal{E}_{2}}\) \(\boldsymbol {\Theta_{\infty}}\) \(\boldsymbol {\Theta_{2}}\)
4 0 0 5.82e−02 3.52e−02
8 0 0 2.39e−02 1.16e−02 1.3 1.6
16 0 0 6.07e−03 2.38e−03 2.0 2.3
32 0 0 6.00e−04 2.02e−04 3.3 3.6
4 0.440 0.2900 7.39e−02 4.01e−02
8 0.280 0.2700 8.58e−03 1.59e−03 3.1 4.7
16 0.103 0.1020 2.61e−04 8.93e−05 4.9 4.2
32 0.000 0.0423 4.35e−05 5.15e−06 2.6 4.1